Factors of 160
Did you know that the sum of the first eleven primes and the sum of the cubes of first three prime numbers is 160? In this lesson, we will calculate the factors of 160, prime factors of 160, and factors of 160 in pairs along with solved examples for a better understanding.
- Factors of 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, and 160
- Prime Factorization of 160: 21 = 25 × 5
| 1. | What Are the Factors of 160? |
| 2. | How to Calculate Factors of 160? |
| 3. | Factors of 160 by Prime Factorization |
| 4. | Factors of 160 in Pairs |
| 5. | FAQs on Factors of 160 |
What Are the Factors of 160?
160 is an even composite number. As it is even, it will have 2 as its factor. To understand why it is composite, let's recall the definition of a composite number. A number is said to be composite if it has more than two factors. 160 has more than 2 factors, hence it is a composite number. Factors of 160 are all the integers that 160 can be divided into.
The factors of 160 are written as 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, and 160.
How to Calculate the Factors of 160?
We can use different methods like prime factorization and the division method to calculate the factors of 160. In prime factorization, we express 160 as a product of its prime factors, and in the division method, we see what numbers divide 160 exactly without a remainder. Let us check divisibility of 160 with various numbers and find all the factors of 160.
Hence, the factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, and 160.
Explore factors using illustrations and interactive examples.
- Factors of 150 - The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
- Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75
- Factors of 25 - The factors of 25 are 1, 5, 25
- Factors of 180 - The factors of 180 are , 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
- Factors of 225 - The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 50, 75, 225
- Factors of 35 - The factors of 35 are 1, 5, 7, 35
Factors of 160 by Prime Factorization
Prime factorization means expressing a number in terms of the product of its prime factors. We can do this by division method or factor tree. The number 160 is divided by the smallest prime number that divides 160 exactly, i.e., it leaves a remainder 0. The quotient is then divided by the smallest or second smallest prime number and the process continues till the quotient gets undividable.
Let us divide 160 by the prime number 2.
160/2 = 80
Now we need to divide the quotient 80 by the next least prime number.
80/2 = 40
Again quotient 40 is divisible by 2.
40/2 = 20
And if we keep on dividing, we get
20/2 = 10,
10/2 = 5
5 is a prime number we cannot divide further. Therefore, the prime factors of 160 are 2 and 5 only. But exponentially it can be written as 160 = 25 × 5
Now that we have done the prime factorization of 160, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.
Factors of 160 in Pairs
The pair of numbers which gives 160 when multiplied is known as factor pairs of 160. The following are the factors of 160 in pairs.
| The Product Form of 160 | Pair Factor |
| 1 × 160 = 160 | 1, 160 |
| 2 × 80 = 160 | 2, 80 |
| 4 × 40 = 160 | 4, 40 |
| 5 × 32 = 160 | 5, 32 |
| 8 × 20 = 160 | 8, 20 |
| 10 × 16 = 160 | 10, 16 |
| 16 × 10 = 160 | 16, 10 |
| 20 × 8 = 160 | 20, 8 |
| 32 × 5 = 160 | 32, 5 |
| 40 × 4 = 160 | 40, 4 |
| 80 × 2 = 160 | 80, 2 |
| 160 × 1 = 160 | 160, 1 |
Observe in the table above, after 10 × 16, the factors start repeating except the order. So, it is enough to find factors until (10,16).
If we consider negative integers, then both the numbers in the pair factors will be negative.
So, we can have factor pairs of 160 as (-1, -160), (-2, -80), (-4, -40), (-5, -32), (-8, -20), and (-10, -16).
Important Notes:
- The numbers which we multiply to get 160 are the factors of 160.
- Factors of 160 are written as 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, and 160.
- The number itself is a factor of the number as it divides itself exactly.
- Factor pairs are the pairs of two numbers which, when multiplied, give the number. Factor pairs of 160 are (1, 160), (2, 80), (4, 40), (5, 32), (8, 20), and (10, 16).
FAQs on Factors of 160
What are the factors of 160?
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, and 160.
What is the highest common factor of 160 and 180?
We will now calculate the prime factors of 160 and 180, then find the greatest common factor of the numbers by matching the biggest common factor of 160 and 180.
160 = 2 × 2 × 2 × 2 × 2 × 5
180 = 2 × 2 × 3 × 3 × 5
Therefore, the highest common factor of 160 and 180 is 2 × 2 × 5 = 20.
Is 160 a perfect square?
160 is not a perfect square because its square root is not a whole number.
What is the sum of all prime factors of 160?
The sum of all prime factors of 160 is 2 + 2 + 2 + 2 + 2 + 5 = 15.
What are the common factors of 160 and 180?
Factors of 160 = 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The common factors of 160 and 180 are 1, 2, 4, 5, 10, and 20.